Chapter 12.4, Problem 10P

Make a box and whisker plot to represent each set of data.

Winning times (min): 148 148 158 149 164 163 149 156

To determine

Find minimum , first quartile , median , third quartile , and maximum of the given data set and draw box-and-whisker plot.

Answer to Problem 10P

Minimum = 148

First quartile = 148.5

Median = 152.5

Third quartile = 160.5

Maximum = 164

Explanation of Solution

Given:

148 , 148 , 158 , 149 , 164 , 163 , 149 , 156

Calculation:

Arrange the data in ascending order:

148 , 148 , 149 , 149 , 156 , 158 , 163 , 164

The minimum is 148.

The first quartile is the median of the lower half of the data set.

Since the total entries are 8, which is even , So, the lower half is the first $\frac{8}{2}=4$ entries.

So , the first quartile is $\frac{148+149}{2}=148.5$

Median = The mean of $\frac{8}{2}=4^{th}\&5^{th}$ entry = $\frac{149+156}{2}=152.5$

The third quartile is the median of the upper half of the data set.

Since the total entries are 8, which is even , So, the upper half is the last $\frac{8}{2}=4$ entries.

So , the third quartile is $\frac{158+163}{2}=160.5$

The maximum is 164